Finite temperature behaviors of q-deformed Fermi gases

During the last three decades, nonstandard statistics for indistinguishable quantum particles has attracted wide attention and research interests from many institutions. Among these new types of statistics, the q-deformed Bose and Fermi statistics, originated from the study of quantum algebra, are being applied in more and more physical systems. In this paper, we construct a q-deformed generalization of the BCS-Leggett theory for ultracold Fermi gases based on our previously constructed q-deformed BCS theory. Some interesting features of this q-deformed interacting quantum gas are obtained by numerical analysis. For example, in the ordinary Bose-Einstein Condensation regime, the gas presents a fermionic feature instead of bosonic feature if the deformation parameter is tuned suitably, which might be referred to as the q-induced "Bose-Fermi" crossover. Conversely, a weak sign of the "Fermi-Bose" crossover is also found in the ordinary weak fermionic regime.